pdfgld {lmomco} | R Documentation

## Probability Density Function of the Generalized Lambda Distribution

### Description

This function computes the probability density function of the Generalized Lambda distribution given parameters (xi, α, kappa, and h) of the distribution computed by `pargld` or similar. The probability density function is

f(x) = {[(kappa(F)^{kappa-1} + h(F)^{h-1})*α]}^-1 mbox{at } x = Q(F)

where f(x) is the probability density function at x, Q(F is the quantile function for nonexceedance probability F.

### Usage

    pdfgld(x, gldpara, paracheck)

### Arguments

`x` | A real value.
`gldpara` | The parameters from `pargld` or similar.
`paracheck` | A logical switch as to whether the validity of the parameters should be checked. Default is `paracheck=TRUE`. This switch is made so that the root solution needed for `cdfgld` exhibits an extreme speed increase because of the repeated calls to `quagld`.

### Value

Probability density (f) for x.

### Author(s)

W.H. Asquith

### References

Karian, Z.A., and Dudewicz, E.J., 2000, Fitting statistical distributions—The generalized lambda distribution and generalized bootstrap methods: CRC Press, Boca Raton, FL, 438 p.

### See Also

`cdfgld`, `quagld`, `lmomgld`, `pargld`

### Examples

    # Using Karian and Dudewicz, 2000, p. 10
    gld <- vec2par(c(0.0305,1/1.3673,0.004581,0.01020),type='gld')
    quagld(0.25,gld) # which equals about 0.028013 as reported by K&D
    pdfgld(0.028013,gld) # which equals about 43.04 as reported by K&D
    F <- seq(.001,.999,by=.001)
    x <- quagld(F,gld)
    #plot(x,pdfgld(x,gld),type='l',xlim=c(0,.1))

[Package lmomco version 0.92 Index]